**CBSE NCERT Solutions Chapter 5 Arithmetic Progressions Exercise 5.2 Question 8
**

**8. An AP consists of 50 terms of which 3rd term is 12 and the last term is 106. Find the 29th term.**

**Solution:**

An AP consists of 50 terms and the 50th term is equal to 106.

It is also given that . { is the 3rd term of AP}

**Using formula** , to find nth term of arithmetic progression,** we get**

And

And

And

These are equations consisting of two variables. Lets solve them using substitution method.

Using equation , we get

Putting value of in the equation , we get

Putting value of in the equation, , we get

Therefore, First term and Common difference

**To find 29th term, we use formula** which is used to find nth term of arithmetic progression, we get

Therefore, 29th term of AP is equal to .

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